--Disease Characteristics-- Immunoglobulin G or immunoglobulin A (IgA) multiple myeloma Low or intermediate risk disease based on the following criteria: Cytogenetics: no translocations, 11q, or -13/13q- Beta-2 microglobulin less than 2.5 mg/L before the first autologous peripheral blood stem cell transplantation (APBSCT) M-protein concentration in harvested plasma greater than 50% of total immunoglobulin of corresponding isotype (M-protein must be able to be purified by protein A- or anti-IgA-sepharose) Patients achieving partial or complete response after the first APBSCT eligible --Prior/Concurrent Therapy-- Biologic therapy: See Disease Characteristics No prior APBSCT with CD34 selected stem cells Chemotherapy: Not specified Endocrine therapy: Steroids must be discontinued at least 4 weeks prior to vaccination No concurrent steroids Radiotherapy: Not specified Surgery: Not specified Other: Any prior therapy must be completed at least 8 weeks prior to second APBSCT Recovered from the toxic effects of prior therapy No concurrent aspirin or nonsteroidal antiinflammatory drugs --Patient Characteristics-- Age: 18 and over Performance status: Karnofsky 70-100% Life expectancy: More than 8 weeks Hepatic: Bilirubin less than 2.0 mg/dL and not rising for at least 2-4 weeks before transplantation SGOT no greater than 4 times upper limit of normal and not rising for at least 2-4 weeks before transplantation Renal: Creatinine less than 2 times normal and not rising for at least 2-4 weeks before transplantation OR Creatinine clearance greater than 40 mL/min Cardiovascular: LVEF greater than 50% by MUGA scan Pulmonary: DLCO greater than 50% predicted Other: No other medical condition that would increase risk of transplantation HIV negative Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception